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Theorem ancoms 54
Description: Swap the two elements of a context. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypothesis
Ref Expression
ancoms.1 (R, S)⊧T
Assertion
Ref Expression
ancoms (S, R)⊧T

Proof of Theorem ancoms
StepHypRef Expression
1 ancoms.1 . . . . 5 (R, S)⊧T
21ax-cb1 29 . . . 4 (R, S):∗
32wctr 34 . . 3 S:∗
42wctl 33 . . 3 R:∗
53, 4simpr 23 . 2 (S, R)⊧R
63, 4simpl 22 . 2 (S, R)⊧S
75, 6, 1syl2anc 19 1 (S, R)⊧T
Colors of variables: type var term
Syntax hints:  kct 10  wffMMJ2 11
This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-cb1 29  ax-wctl 31  ax-wctr 32
This theorem is referenced by:  adantl  56  anasss  61
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